The degree distribution of the generalized duplication model

CombiMotif: A new algorithm for network motifs discovery in protein–protein interaction networks

“…Protein-protein interaction (PPI) networks of many species have been shown to share similar global topological features, such as small-world effect [1,2], power-law degree distribution [3][4][5], and large clustering coefficient [6]. However, some of these networks can have significant differences in terms of local structures; for instance, the number of specific subgraphs can vary significantly among PPI networks.…”

Preferential duplication graphs

“…Indeed, graph growing models based on vertex duplications have been the subject of investigation over recent years (for example [1,5,6,7,10]). In most of these models vertices are chosen for duplication according to a uniform distribution, while in the model of [5] all vertices are duplicated simultaneously.…”

Degree distribution of large networks generated by the partial duplication model

“…This mechanism was formulated into a network growth model by [11]. Since then, many variations and extensions have been proposed and studied [12][13][14][15][16][17][18]. We refer to this family of network growth models as duplication and divergence (DD) models.…”

“…Instead, the attention has been centered on the limiting degree distribution, which provides valuable information on the long run behavior of the model [15,16,21].…”

“…For the special case k = 0, the existence of f (0) = lim t→∞ f t (0) was proved by [16] by showing {f t (0)} t≥0 is indeed a non-decreasing sequence. However, the other cases remained open and it was often assumed that they do exist in previous studies.…”